Properties

Label 2025.bu
Modulus $2025$
Conductor $2025$
Order $540$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2025, base_ring=CyclotomicField(540))
 
M = H._module
 
chi = DirichletCharacter(H, M([80,513]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(13,2025))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2025\)
Conductor: \(2025\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(540\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{540})$
Fixed field: Number field defined by a degree 540 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(7\) \(8\) \(11\) \(13\) \(14\) \(16\) \(17\) \(19\)
\(\chi_{2025}(13,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{540}\right)\) \(e\left(\frac{53}{270}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{53}{180}\right)\) \(e\left(\frac{17}{135}\right)\) \(e\left(\frac{127}{540}\right)\) \(e\left(\frac{59}{270}\right)\) \(e\left(\frac{53}{135}\right)\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{19}{90}\right)\)
\(\chi_{2025}(22,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{540}\right)\) \(e\left(\frac{59}{270}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{59}{180}\right)\) \(e\left(\frac{131}{135}\right)\) \(e\left(\frac{121}{540}\right)\) \(e\left(\frac{137}{270}\right)\) \(e\left(\frac{59}{135}\right)\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{67}{90}\right)\)
\(\chi_{2025}(52,\cdot)\) \(-1\) \(1\) \(e\left(\frac{127}{540}\right)\) \(e\left(\frac{127}{270}\right)\) \(e\left(\frac{23}{108}\right)\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{28}{135}\right)\) \(e\left(\frac{233}{540}\right)\) \(e\left(\frac{121}{270}\right)\) \(e\left(\frac{127}{135}\right)\) \(e\left(\frac{137}{180}\right)\) \(e\left(\frac{71}{90}\right)\)
\(\chi_{2025}(58,\cdot)\) \(-1\) \(1\) \(e\left(\frac{461}{540}\right)\) \(e\left(\frac{191}{270}\right)\) \(e\left(\frac{1}{108}\right)\) \(e\left(\frac{101}{180}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{259}{540}\right)\) \(e\left(\frac{233}{270}\right)\) \(e\left(\frac{56}{135}\right)\) \(e\left(\frac{31}{180}\right)\) \(e\left(\frac{43}{90}\right)\)
\(\chi_{2025}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{251}{540}\right)\) \(e\left(\frac{251}{270}\right)\) \(e\left(\frac{31}{108}\right)\) \(e\left(\frac{71}{180}\right)\) \(e\left(\frac{134}{135}\right)\) \(e\left(\frac{469}{540}\right)\) \(e\left(\frac{203}{270}\right)\) \(e\left(\frac{116}{135}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{73}{90}\right)\)
\(\chi_{2025}(88,\cdot)\) \(-1\) \(1\) \(e\left(\frac{133}{540}\right)\) \(e\left(\frac{133}{270}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{7}{135}\right)\) \(e\left(\frac{227}{540}\right)\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{133}{135}\right)\) \(e\left(\frac{23}{180}\right)\) \(e\left(\frac{29}{90}\right)\)
\(\chi_{2025}(97,\cdot)\) \(-1\) \(1\) \(e\left(\frac{499}{540}\right)\) \(e\left(\frac{229}{270}\right)\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{76}{135}\right)\) \(e\left(\frac{401}{540}\right)\) \(e\left(\frac{97}{270}\right)\) \(e\left(\frac{94}{135}\right)\) \(e\left(\frac{89}{180}\right)\) \(e\left(\frac{77}{90}\right)\)
\(\chi_{2025}(103,\cdot)\) \(-1\) \(1\) \(e\left(\frac{329}{540}\right)\) \(e\left(\frac{59}{270}\right)\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{149}{180}\right)\) \(e\left(\frac{131}{135}\right)\) \(e\left(\frac{391}{540}\right)\) \(e\left(\frac{137}{270}\right)\) \(e\left(\frac{59}{135}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{67}{90}\right)\)
\(\chi_{2025}(112,\cdot)\) \(-1\) \(1\) \(e\left(\frac{443}{540}\right)\) \(e\left(\frac{173}{270}\right)\) \(e\left(\frac{19}{108}\right)\) \(e\left(\frac{83}{180}\right)\) \(e\left(\frac{2}{135}\right)\) \(e\left(\frac{277}{540}\right)\) \(e\left(\frac{269}{270}\right)\) \(e\left(\frac{38}{135}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{79}{90}\right)\)
\(\chi_{2025}(133,\cdot)\) \(-1\) \(1\) \(e\left(\frac{181}{540}\right)\) \(e\left(\frac{181}{270}\right)\) \(e\left(\frac{77}{108}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{109}{135}\right)\) \(e\left(\frac{179}{540}\right)\) \(e\left(\frac{13}{270}\right)\) \(e\left(\frac{46}{135}\right)\) \(e\left(\frac{11}{180}\right)\) \(e\left(\frac{53}{90}\right)\)
\(\chi_{2025}(142,\cdot)\) \(-1\) \(1\) \(e\left(\frac{331}{540}\right)\) \(e\left(\frac{61}{270}\right)\) \(e\left(\frac{71}{108}\right)\) \(e\left(\frac{151}{180}\right)\) \(e\left(\frac{124}{135}\right)\) \(e\left(\frac{29}{540}\right)\) \(e\left(\frac{73}{270}\right)\) \(e\left(\frac{61}{135}\right)\) \(e\left(\frac{41}{180}\right)\) \(e\left(\frac{83}{90}\right)\)
\(\chi_{2025}(148,\cdot)\) \(-1\) \(1\) \(e\left(\frac{197}{540}\right)\) \(e\left(\frac{197}{270}\right)\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{17}{180}\right)\) \(e\left(\frac{53}{135}\right)\) \(e\left(\frac{523}{540}\right)\) \(e\left(\frac{41}{270}\right)\) \(e\left(\frac{62}{135}\right)\) \(e\left(\frac{7}{180}\right)\) \(e\left(\frac{1}{90}\right)\)
\(\chi_{2025}(178,\cdot)\) \(-1\) \(1\) \(e\left(\frac{229}{540}\right)\) \(e\left(\frac{229}{270}\right)\) \(e\left(\frac{101}{108}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{76}{135}\right)\) \(e\left(\frac{131}{540}\right)\) \(e\left(\frac{97}{270}\right)\) \(e\left(\frac{94}{135}\right)\) \(e\left(\frac{179}{180}\right)\) \(e\left(\frac{77}{90}\right)\)
\(\chi_{2025}(187,\cdot)\) \(-1\) \(1\) \(e\left(\frac{163}{540}\right)\) \(e\left(\frac{163}{270}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{37}{135}\right)\) \(e\left(\frac{197}{540}\right)\) \(e\left(\frac{49}{270}\right)\) \(e\left(\frac{28}{135}\right)\) \(e\left(\frac{173}{180}\right)\) \(e\left(\frac{89}{90}\right)\)
\(\chi_{2025}(202,\cdot)\) \(-1\) \(1\) \(e\left(\frac{287}{540}\right)\) \(e\left(\frac{17}{270}\right)\) \(e\left(\frac{103}{108}\right)\) \(e\left(\frac{107}{180}\right)\) \(e\left(\frac{8}{135}\right)\) \(e\left(\frac{433}{540}\right)\) \(e\left(\frac{131}{270}\right)\) \(e\left(\frac{17}{135}\right)\) \(e\left(\frac{97}{180}\right)\) \(e\left(\frac{1}{90}\right)\)
\(\chi_{2025}(223,\cdot)\) \(-1\) \(1\) \(e\left(\frac{277}{540}\right)\) \(e\left(\frac{7}{270}\right)\) \(e\left(\frac{17}{108}\right)\) \(e\left(\frac{97}{180}\right)\) \(e\left(\frac{43}{135}\right)\) \(e\left(\frac{83}{540}\right)\) \(e\left(\frac{181}{270}\right)\) \(e\left(\frac{7}{135}\right)\) \(e\left(\frac{167}{180}\right)\) \(e\left(\frac{11}{90}\right)\)
\(\chi_{2025}(238,\cdot)\) \(-1\) \(1\) \(e\left(\frac{473}{540}\right)\) \(e\left(\frac{203}{270}\right)\) \(e\left(\frac{61}{108}\right)\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{32}{135}\right)\) \(e\left(\frac{247}{540}\right)\) \(e\left(\frac{119}{270}\right)\) \(e\left(\frac{68}{135}\right)\) \(e\left(\frac{163}{180}\right)\) \(e\left(\frac{49}{90}\right)\)
\(\chi_{2025}(247,\cdot)\) \(-1\) \(1\) \(e\left(\frac{479}{540}\right)\) \(e\left(\frac{209}{270}\right)\) \(e\left(\frac{91}{108}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{11}{135}\right)\) \(e\left(\frac{241}{540}\right)\) \(e\left(\frac{197}{270}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{49}{180}\right)\) \(e\left(\frac{7}{90}\right)\)
\(\chi_{2025}(277,\cdot)\) \(-1\) \(1\) \(e\left(\frac{367}{540}\right)\) \(e\left(\frac{97}{270}\right)\) \(e\left(\frac{35}{108}\right)\) \(e\left(\frac{7}{180}\right)\) \(e\left(\frac{133}{135}\right)\) \(e\left(\frac{533}{540}\right)\) \(e\left(\frac{1}{270}\right)\) \(e\left(\frac{97}{135}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{11}{90}\right)\)
\(\chi_{2025}(283,\cdot)\) \(-1\) \(1\) \(e\left(\frac{341}{540}\right)\) \(e\left(\frac{71}{270}\right)\) \(e\left(\frac{49}{108}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{89}{135}\right)\) \(e\left(\frac{379}{540}\right)\) \(e\left(\frac{23}{270}\right)\) \(e\left(\frac{71}{135}\right)\) \(e\left(\frac{151}{180}\right)\) \(e\left(\frac{73}{90}\right)\)
\(\chi_{2025}(292,\cdot)\) \(-1\) \(1\) \(e\left(\frac{131}{540}\right)\) \(e\left(\frac{131}{270}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{131}{180}\right)\) \(e\left(\frac{14}{135}\right)\) \(e\left(\frac{49}{540}\right)\) \(e\left(\frac{263}{270}\right)\) \(e\left(\frac{131}{135}\right)\) \(e\left(\frac{1}{180}\right)\) \(e\left(\frac{13}{90}\right)\)
\(\chi_{2025}(313,\cdot)\) \(-1\) \(1\) \(e\left(\frac{373}{540}\right)\) \(e\left(\frac{103}{270}\right)\) \(e\left(\frac{65}{108}\right)\) \(e\left(\frac{13}{180}\right)\) \(e\left(\frac{112}{135}\right)\) \(e\left(\frac{527}{540}\right)\) \(e\left(\frac{79}{270}\right)\) \(e\left(\frac{103}{135}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{59}{90}\right)\)
\(\chi_{2025}(322,\cdot)\) \(-1\) \(1\) \(e\left(\frac{199}{540}\right)\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{59}{108}\right)\) \(e\left(\frac{19}{180}\right)\) \(e\left(\frac{46}{135}\right)\) \(e\left(\frac{161}{540}\right)\) \(e\left(\frac{247}{270}\right)\) \(e\left(\frac{64}{135}\right)\) \(e\left(\frac{29}{180}\right)\) \(e\left(\frac{17}{90}\right)\)
\(\chi_{2025}(328,\cdot)\) \(-1\) \(1\) \(e\left(\frac{209}{540}\right)\) \(e\left(\frac{209}{270}\right)\) \(e\left(\frac{37}{108}\right)\) \(e\left(\frac{29}{180}\right)\) \(e\left(\frac{11}{135}\right)\) \(e\left(\frac{511}{540}\right)\) \(e\left(\frac{197}{270}\right)\) \(e\left(\frac{74}{135}\right)\) \(e\left(\frac{139}{180}\right)\) \(e\left(\frac{7}{90}\right)\)
\(\chi_{2025}(337,\cdot)\) \(-1\) \(1\) \(e\left(\frac{323}{540}\right)\) \(e\left(\frac{53}{270}\right)\) \(e\left(\frac{67}{108}\right)\) \(e\left(\frac{143}{180}\right)\) \(e\left(\frac{17}{135}\right)\) \(e\left(\frac{397}{540}\right)\) \(e\left(\frac{59}{270}\right)\) \(e\left(\frac{53}{135}\right)\) \(e\left(\frac{133}{180}\right)\) \(e\left(\frac{19}{90}\right)\)
\(\chi_{2025}(358,\cdot)\) \(-1\) \(1\) \(e\left(\frac{421}{540}\right)\) \(e\left(\frac{151}{270}\right)\) \(e\left(\frac{89}{108}\right)\) \(e\left(\frac{61}{180}\right)\) \(e\left(\frac{79}{135}\right)\) \(e\left(\frac{479}{540}\right)\) \(e\left(\frac{163}{270}\right)\) \(e\left(\frac{16}{135}\right)\) \(e\left(\frac{131}{180}\right)\) \(e\left(\frac{83}{90}\right)\)
\(\chi_{2025}(367,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{540}\right)\) \(e\left(\frac{31}{270}\right)\) \(e\left(\frac{83}{108}\right)\) \(e\left(\frac{31}{180}\right)\) \(e\left(\frac{94}{135}\right)\) \(e\left(\frac{329}{540}\right)\) \(e\left(\frac{223}{270}\right)\) \(e\left(\frac{31}{135}\right)\) \(e\left(\frac{161}{180}\right)\) \(e\left(\frac{23}{90}\right)\)
\(\chi_{2025}(373,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{540}\right)\) \(e\left(\frac{77}{270}\right)\) \(e\left(\frac{25}{108}\right)\) \(e\left(\frac{77}{180}\right)\) \(e\left(\frac{68}{135}\right)\) \(e\left(\frac{103}{540}\right)\) \(e\left(\frac{101}{270}\right)\) \(e\left(\frac{77}{135}\right)\) \(e\left(\frac{127}{180}\right)\) \(e\left(\frac{31}{90}\right)\)
\(\chi_{2025}(403,\cdot)\) \(-1\) \(1\) \(e\left(\frac{469}{540}\right)\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{109}{180}\right)\) \(e\left(\frac{46}{135}\right)\) \(e\left(\frac{431}{540}\right)\) \(e\left(\frac{247}{270}\right)\) \(e\left(\frac{64}{135}\right)\) \(e\left(\frac{119}{180}\right)\) \(e\left(\frac{17}{90}\right)\)
\(\chi_{2025}(412,\cdot)\) \(-1\) \(1\) \(e\left(\frac{403}{540}\right)\) \(e\left(\frac{133}{270}\right)\) \(e\left(\frac{107}{108}\right)\) \(e\left(\frac{43}{180}\right)\) \(e\left(\frac{7}{135}\right)\) \(e\left(\frac{497}{540}\right)\) \(e\left(\frac{199}{270}\right)\) \(e\left(\frac{133}{135}\right)\) \(e\left(\frac{113}{180}\right)\) \(e\left(\frac{29}{90}\right)\)
\(\chi_{2025}(427,\cdot)\) \(-1\) \(1\) \(e\left(\frac{167}{540}\right)\) \(e\left(\frac{167}{270}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{167}{180}\right)\) \(e\left(\frac{23}{135}\right)\) \(e\left(\frac{13}{540}\right)\) \(e\left(\frac{191}{270}\right)\) \(e\left(\frac{32}{135}\right)\) \(e\left(\frac{37}{180}\right)\) \(e\left(\frac{31}{90}\right)\)